Refined equivalent single layer formulations and finite elements for smart laminates free vibrations

Abstract

A family of 2D refined equivalent single layer models for multilayered and functionally graded smart magneto–electro-elastic plates is presented. They are based on variable kinematics and quasi-static behavior for the electromagnetic fields. First, the electromagnetic state of the plate is determined by solving the strong form of the electromagnetic governing equations coupled with the corresponding interface continuity conditions and external boundary conditions. The electromagnetic state is then condensed into the plate kinematics, whose governing equations can be written using the generalized principle of virtual displacements. The procedure identifies an effective elastic plate kinematically equivalent to the original smart plate. The effective plate is characterized by inertia, stiffness and loading properties which take the multifield coupling effects into account through their definitions, which involve the electromagnetic coefficients appearing in the smart materials constitutive law. The proposed model extends the techniques and tools available for the assessment of the mechanical behavior of multilayered composite plates to smart laminates. Additionally, finite elements for the proposed single layer models are formulated and validated against available benchmark 3D solutions.